The first study of the two-dimensional electron gas in the surface layers on zero-gap HgMnTe is carried out experimentally (by the magnetocapacitance spectroscopy method) and theoretically. The exchange interaction is manifested only in the temperature shift of beat nodes of magneto-oscillations. Information about exchange effects is obtained only by our modelling of oscillations, because any pronounced changes in the position of oscillations are not observed and the separate spin components are not resolved. The theory for the description of a spectrum in a magnetic field and magneto-oscillations with allowance for exchange and spin-orbit (SO) interaction for Kane semiconductors with direct and inverted bands is advanced. The modelling shows that the SO splitting far exceeds the contribution due to exchange interaction. The comparison between experiment and theory for different temperatures and parameters of exchange interaction is reported. The calculated amplitudes of `partial' oscillations for different spin branches of the spectrum are essentially different in accordance with the observed difference in the intensity of corresponding lines in Fourier spectra. The dominant mechanisms of the scattering responsible for the broadening of Landau levels are discussed.